Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2842,2,Mod(1,2842)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2842, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2842.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2842 = 2 \cdot 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2842.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(22.6934842544\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.11348.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 406) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.723742\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2842.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.76342 | 1.59546 | 0.797729 | − | 0.603016i | \(-0.206034\pi\) | ||||
0.797729 | + | 0.603016i | \(0.206034\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.47620 | 1.10739 | 0.553695 | − | 0.832720i | \(-0.313218\pi\) | ||||
0.553695 | + | 0.832720i | \(0.313218\pi\) | |||||||
\(6\) | 2.76342 | 1.12816 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.63646 | 1.54549 | ||||||||
\(10\) | 2.47620 | 0.783042 | ||||||||
\(11\) | 4.76342 | 1.43622 | 0.718112 | − | 0.695928i | \(-0.245007\pi\) | ||||
0.718112 | + | 0.695928i | \(0.245007\pi\) | |||||||
\(12\) | 2.76342 | 0.797729 | ||||||||
\(13\) | −0.155665 | −0.0431736 | −0.0215868 | − | 0.999767i | \(-0.506872\pi\) | ||||
−0.0215868 | + | 0.999767i | \(0.506872\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.84276 | 1.76679 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.23961 | −1.27079 | −0.635396 | − | 0.772186i | \(-0.719163\pi\) | ||||
−0.635396 | + | 0.772186i | \(0.719163\pi\) | |||||||
\(18\) | 4.63646 | 1.09282 | ||||||||
\(19\) | −1.44748 | −0.332076 | −0.166038 | − | 0.986119i | \(-0.553097\pi\) | ||||
−0.166038 | + | 0.986119i | \(0.553097\pi\) | |||||||
\(20\) | 2.47620 | 0.553695 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.76342 | 1.01556 | ||||||||
\(23\) | 0.552516 | 0.115207 | 0.0576037 | − | 0.998340i | \(-0.481654\pi\) | ||||
0.0576037 | + | 0.998340i | \(0.481654\pi\) | |||||||
\(24\) | 2.76342 | 0.564080 | ||||||||
\(25\) | 1.13155 | 0.226311 | ||||||||
\(26\) | −0.155665 | −0.0305283 | ||||||||
\(27\) | 4.52223 | 0.870303 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 6.84276 | 1.24931 | ||||||||
\(31\) | −7.45051 | −1.33815 | −0.669076 | − | 0.743194i | \(-0.733310\pi\) | ||||
−0.669076 | + | 0.743194i | \(0.733310\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 13.1633 | 2.29144 | ||||||||
\(34\) | −5.23961 | −0.898586 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.63646 | 0.772744 | ||||||||
\(37\) | −8.07935 | −1.32824 | −0.664118 | − | 0.747628i | \(-0.731193\pi\) | ||||
−0.664118 | + | 0.747628i | \(0.731193\pi\) | |||||||
\(38\) | −1.44748 | −0.234813 | ||||||||
\(39\) | −0.430166 | −0.0688817 | ||||||||
\(40\) | 2.47620 | 0.391521 | ||||||||
\(41\) | −4.66518 | −0.728578 | −0.364289 | − | 0.931286i | \(-0.618688\pi\) | ||||
−0.364289 | + | 0.931286i | \(0.618688\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.63646 | −0.554556 | −0.277278 | − | 0.960790i | \(-0.589432\pi\) | ||||
−0.277278 | + | 0.960790i | \(0.589432\pi\) | |||||||
\(44\) | 4.76342 | 0.718112 | ||||||||
\(45\) | 11.4808 | 1.71146 | ||||||||
\(46\) | 0.552516 | 0.0814640 | ||||||||
\(47\) | −4.55554 | −0.664494 | −0.332247 | − | 0.943192i | \(-0.607807\pi\) | ||||
−0.332247 | + | 0.943192i | \(0.607807\pi\) | |||||||
\(48\) | 2.76342 | 0.398865 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.13155 | 0.160026 | ||||||||
\(51\) | −14.4792 | −2.02750 | ||||||||
\(52\) | −0.155665 | −0.0215868 | ||||||||
\(53\) | −7.16329 | −0.983954 | −0.491977 | − | 0.870608i | \(-0.663726\pi\) | ||||
−0.491977 | + | 0.870608i | \(0.663726\pi\) | |||||||
\(54\) | 4.52223 | 0.615397 | ||||||||
\(55\) | 11.7952 | 1.59046 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | −6.05523 | −0.788324 | −0.394162 | − | 0.919041i | \(-0.628965\pi\) | ||||
−0.394162 | + | 0.919041i | \(0.628965\pi\) | |||||||
\(60\) | 6.84276 | 0.883397 | ||||||||
\(61\) | 9.12695 | 1.16859 | 0.584293 | − | 0.811543i | \(-0.301372\pi\) | ||||
0.584293 | + | 0.811543i | \(0.301372\pi\) | |||||||
\(62\) | −7.45051 | −0.946216 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.385456 | −0.0478100 | ||||||||
\(66\) | 13.1633 | 1.62029 | ||||||||
\(67\) | 14.7906 | 1.80695 | 0.903477 | − | 0.428637i | \(-0.141006\pi\) | ||||
0.903477 | + | 0.428637i | \(0.141006\pi\) | |||||||
\(68\) | −5.23961 | −0.635396 | ||||||||
\(69\) | 1.52683 | 0.183809 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.6154 | 1.61585 | 0.807924 | − | 0.589286i | \(-0.200591\pi\) | ||||
0.807924 | + | 0.589286i | \(0.200591\pi\) | |||||||
\(72\) | 4.63646 | 0.546412 | ||||||||
\(73\) | 0.439855 | 0.0514811 | 0.0257406 | − | 0.999669i | \(-0.491806\pi\) | ||||
0.0257406 | + | 0.999669i | \(0.491806\pi\) | |||||||
\(74\) | −8.07935 | −0.939205 | ||||||||
\(75\) | 3.12695 | 0.361069 | ||||||||
\(76\) | −1.44748 | −0.166038 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.430166 | −0.0487067 | ||||||||
\(79\) | −17.0107 | −1.91385 | −0.956924 | − | 0.290338i | \(-0.906232\pi\) | ||||
−0.956924 | + | 0.290338i | \(0.906232\pi\) | |||||||
\(80\) | 2.47620 | 0.276847 | ||||||||
\(81\) | −1.41260 | −0.156955 | ||||||||
\(82\) | −4.66518 | −0.515183 | ||||||||
\(83\) | −6.10346 | −0.669942 | −0.334971 | − | 0.942229i | \(-0.608726\pi\) | ||||
−0.334971 | + | 0.942229i | \(0.608726\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.9743 | −1.40726 | ||||||||
\(86\) | −3.63646 | −0.392130 | ||||||||
\(87\) | 2.76342 | 0.296269 | ||||||||
\(88\) | 4.76342 | 0.507782 | ||||||||
\(89\) | −10.1920 | −1.08035 | −0.540175 | − | 0.841553i | \(-0.681642\pi\) | ||||
−0.540175 | + | 0.841553i | \(0.681642\pi\) | |||||||
\(90\) | 11.4808 | 1.21018 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.552516 | 0.0576037 | ||||||||
\(93\) | −20.5889 | −2.13497 | ||||||||
\(94\) | −4.55554 | −0.469868 | ||||||||
\(95\) | −3.58426 | −0.367737 | ||||||||
\(96\) | 2.76342 | 0.282040 | ||||||||
\(97\) | 4.66518 | 0.473677 | 0.236838 | − | 0.971549i | \(-0.423889\pi\) | ||||
0.236838 | + | 0.971549i | \(0.423889\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 22.0854 | 2.21967 | ||||||||
\(100\) | 1.13155 | 0.113155 | ||||||||
\(101\) | 8.39988 | 0.835819 | 0.417910 | − | 0.908489i | \(-0.362763\pi\) | ||||
0.417910 | + | 0.908489i | \(0.362763\pi\) | |||||||
\(102\) | −14.4792 | −1.43366 | ||||||||
\(103\) | 12.7331 | 1.25463 | 0.627316 | − | 0.778765i | \(-0.284153\pi\) | ||||
0.627316 | + | 0.778765i | \(0.284153\pi\) | |||||||
\(104\) | −0.155665 | −0.0152642 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.16329 | −0.695761 | ||||||||
\(107\) | 1.36814 | 0.132263 | 0.0661314 | − | 0.997811i | \(-0.478934\pi\) | ||||
0.0661314 | + | 0.997811i | \(0.478934\pi\) | |||||||
\(108\) | 4.52223 | 0.435152 | ||||||||
\(109\) | 8.53143 | 0.817163 | 0.408582 | − | 0.912722i | \(-0.366024\pi\) | ||||
0.408582 | + | 0.912722i | \(0.366024\pi\) | |||||||
\(110\) | 11.7952 | 1.12462 | ||||||||
\(111\) | −22.3266 | −2.11915 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.0061 | −1.31758 | −0.658789 | − | 0.752327i | \(-0.728931\pi\) | ||||
−0.658789 | + | 0.752327i | \(0.728931\pi\) | |||||||
\(114\) | −4.00000 | −0.374634 | ||||||||
\(115\) | 1.36814 | 0.127580 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | −0.721733 | −0.0667243 | ||||||||
\(118\) | −6.05523 | −0.557430 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.84276 | 0.624656 | ||||||||
\(121\) | 11.6901 | 1.06274 | ||||||||
\(122\) | 9.12695 | 0.826315 | ||||||||
\(123\) | −12.8918 | −1.16242 | ||||||||
\(124\) | −7.45051 | −0.669076 | ||||||||
\(125\) | −9.57904 | −0.856775 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.4792 | 1.63977 | 0.819883 | − | 0.572531i | \(-0.194038\pi\) | ||||
0.819883 | + | 0.572531i | \(0.194038\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −10.0491 | −0.884770 | ||||||||
\(130\) | −0.385456 | −0.0338068 | ||||||||
\(131\) | 14.2472 | 1.24479 | 0.622394 | − | 0.782704i | \(-0.286160\pi\) | ||||
0.622394 | + | 0.782704i | \(0.286160\pi\) | |||||||
\(132\) | 13.1633 | 1.14572 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 14.7906 | 1.27771 | ||||||||
\(135\) | 11.1979 | 0.963764 | ||||||||
\(136\) | −5.23961 | −0.449293 | ||||||||
\(137\) | 11.8382 | 1.01140 | 0.505701 | − | 0.862709i | \(-0.331234\pi\) | ||||
0.505701 | + | 0.862709i | \(0.331234\pi\) | |||||||
\(138\) | 1.52683 | 0.129972 | ||||||||
\(139\) | −3.31290 | −0.280997 | −0.140498 | − | 0.990081i | \(-0.544870\pi\) | ||||
−0.140498 | + | 0.990081i | \(0.544870\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.5889 | −1.06017 | ||||||||
\(142\) | 13.6154 | 1.14258 | ||||||||
\(143\) | −0.741495 | −0.0620069 | ||||||||
\(144\) | 4.63646 | 0.386372 | ||||||||
\(145\) | 2.47620 | 0.205637 | ||||||||
\(146\) | 0.439855 | 0.0364026 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.07935 | −0.664118 | ||||||||
\(149\) | 11.7377 | 0.961592 | 0.480796 | − | 0.876832i | \(-0.340348\pi\) | ||||
0.480796 | + | 0.876832i | \(0.340348\pi\) | |||||||
\(150\) | 3.12695 | 0.255315 | ||||||||
\(151\) | 21.5110 | 1.75054 | 0.875269 | − | 0.483637i | \(-0.160684\pi\) | ||||
0.875269 | + | 0.483637i | \(0.160684\pi\) | |||||||
\(152\) | −1.44748 | −0.117406 | ||||||||
\(153\) | −24.2933 | −1.96399 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.4489 | −1.48185 | ||||||||
\(156\) | −0.430166 | −0.0344408 | ||||||||
\(157\) | 22.2380 | 1.77479 | 0.887394 | − | 0.461011i | \(-0.152513\pi\) | ||||
0.887394 | + | 0.461011i | \(0.152513\pi\) | |||||||
\(158\) | −17.0107 | −1.35330 | ||||||||
\(159\) | −19.7952 | −1.56986 | ||||||||
\(160\) | 2.47620 | 0.195761 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.41260 | −0.110984 | ||||||||
\(163\) | −18.4489 | −1.44503 | −0.722516 | − | 0.691354i | \(-0.757015\pi\) | ||||
−0.722516 | + | 0.691354i | \(0.757015\pi\) | |||||||
\(164\) | −4.66518 | −0.364289 | ||||||||
\(165\) | 32.5949 | 2.53751 | ||||||||
\(166\) | −6.10346 | −0.473720 | ||||||||
\(167\) | 21.5995 | 1.67142 | 0.835710 | − | 0.549170i | \(-0.185056\pi\) | ||||
0.835710 | + | 0.549170i | \(0.185056\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9758 | −0.998136 | ||||||||
\(170\) | −12.9743 | −0.995085 | ||||||||
\(171\) | −6.71121 | −0.513219 | ||||||||
\(172\) | −3.63646 | −0.277278 | ||||||||
\(173\) | 1.04980 | 0.0798146 | 0.0399073 | − | 0.999203i | \(-0.487294\pi\) | ||||
0.0399073 | + | 0.999203i | \(0.487294\pi\) | |||||||
\(174\) | 2.76342 | 0.209494 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.76342 | 0.359056 | ||||||||
\(177\) | −16.7331 | −1.25774 | ||||||||
\(178\) | −10.1920 | −0.763923 | ||||||||
\(179\) | 20.1587 | 1.50673 | 0.753366 | − | 0.657602i | \(-0.228429\pi\) | ||||
0.753366 | + | 0.657602i | \(0.228429\pi\) | |||||||
\(180\) | 11.4808 | 0.855728 | ||||||||
\(181\) | −0.155665 | −0.0115705 | −0.00578523 | − | 0.999983i | \(-0.501842\pi\) | ||||
−0.00578523 | + | 0.999983i | \(0.501842\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25.2216 | 1.86443 | ||||||||
\(184\) | 0.552516 | 0.0407320 | ||||||||
\(185\) | −20.0061 | −1.47087 | ||||||||
\(186\) | −20.5889 | −1.50965 | ||||||||
\(187\) | −24.9585 | −1.82514 | ||||||||
\(188\) | −4.55554 | −0.332247 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.58426 | −0.260029 | ||||||||
\(191\) | −8.73313 | −0.631907 | −0.315953 | − | 0.948775i | \(-0.602324\pi\) | ||||
−0.315953 | + | 0.948775i | \(0.602324\pi\) | |||||||
\(192\) | 2.76342 | 0.199432 | ||||||||
\(193\) | −0.742332 | −0.0534342 | −0.0267171 | − | 0.999643i | \(-0.508505\pi\) | ||||
−0.0267171 | + | 0.999643i | \(0.508505\pi\) | |||||||
\(194\) | 4.66518 | 0.334940 | ||||||||
\(195\) | −1.06518 | −0.0762788 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.2692 | −0.731648 | −0.365824 | − | 0.930684i | \(-0.619213\pi\) | ||||
−0.365824 | + | 0.930684i | \(0.619213\pi\) | |||||||
\(198\) | 22.0854 | 1.56954 | ||||||||
\(199\) | −0.574436 | −0.0407207 | −0.0203603 | − | 0.999793i | \(-0.506481\pi\) | ||||
−0.0203603 | + | 0.999793i | \(0.506481\pi\) | |||||||
\(200\) | 1.13155 | 0.0800129 | ||||||||
\(201\) | 40.8724 | 2.88292 | ||||||||
\(202\) | 8.39988 | 0.591013 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −14.4792 | −1.01375 | ||||||||
\(205\) | −11.5519 | −0.806820 | ||||||||
\(206\) | 12.7331 | 0.887159 | ||||||||
\(207\) | 2.56172 | 0.178052 | ||||||||
\(208\) | −0.155665 | −0.0107934 | ||||||||
\(209\) | −6.89497 | −0.476935 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4264 | −0.924312 | −0.462156 | − | 0.886799i | \(-0.652924\pi\) | ||||
−0.462156 | + | 0.886799i | \(0.652924\pi\) | |||||||
\(212\) | −7.16329 | −0.491977 | ||||||||
\(213\) | 37.6249 | 2.57802 | ||||||||
\(214\) | 1.36814 | 0.0935240 | ||||||||
\(215\) | −9.00460 | −0.614109 | ||||||||
\(216\) | 4.52223 | 0.307699 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.53143 | 0.577821 | ||||||||
\(219\) | 1.21550 | 0.0821360 | ||||||||
\(220\) | 11.7952 | 0.795229 | ||||||||
\(221\) | 0.815622 | 0.0548647 | ||||||||
\(222\) | −22.3266 | −1.49846 | ||||||||
\(223\) | −5.67947 | −0.380325 | −0.190163 | − | 0.981753i | \(-0.560902\pi\) | ||||
−0.190163 | + | 0.981753i | \(0.560902\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.24641 | 0.349760 | ||||||||
\(226\) | −14.0061 | −0.931669 | ||||||||
\(227\) | 20.9124 | 1.38801 | 0.694003 | − | 0.719972i | \(-0.255845\pi\) | ||||
0.694003 | + | 0.719972i | \(0.255845\pi\) | |||||||
\(228\) | −4.00000 | −0.264906 | ||||||||
\(229\) | −22.6598 | −1.49740 | −0.748702 | − | 0.662907i | \(-0.769323\pi\) | ||||
−0.748702 | + | 0.662907i | \(0.769323\pi\) | |||||||
\(230\) | 1.36814 | 0.0902124 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | 18.9002 | 1.23819 | 0.619096 | − | 0.785315i | \(-0.287499\pi\) | ||||
0.619096 | + | 0.785315i | \(0.287499\pi\) | |||||||
\(234\) | −0.721733 | −0.0471812 | ||||||||
\(235\) | −11.2804 | −0.735854 | ||||||||
\(236\) | −6.05523 | −0.394162 | ||||||||
\(237\) | −47.0075 | −3.05347 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.4945 | −1.58442 | −0.792208 | − | 0.610251i | \(-0.791069\pi\) | ||||
−0.792208 | + | 0.610251i | \(0.791069\pi\) | |||||||
\(240\) | 6.84276 | 0.441698 | ||||||||
\(241\) | 29.2268 | 1.88266 | 0.941331 | − | 0.337485i | \(-0.109576\pi\) | ||||
0.941331 | + | 0.337485i | \(0.109576\pi\) | |||||||
\(242\) | 11.6901 | 0.751470 | ||||||||
\(243\) | −17.4703 | −1.12072 | ||||||||
\(244\) | 9.12695 | 0.584293 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −12.8918 | −0.821952 | ||||||||
\(247\) | 0.225322 | 0.0143369 | ||||||||
\(248\) | −7.45051 | −0.473108 | ||||||||
\(249\) | −16.8664 | −1.06886 | ||||||||
\(250\) | −9.57904 | −0.605832 | ||||||||
\(251\) | −6.45209 | −0.407252 | −0.203626 | − | 0.979049i | \(-0.565273\pi\) | ||||
−0.203626 | + | 0.979049i | \(0.565273\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.63186 | 0.165464 | ||||||||
\(254\) | 18.4792 | 1.15949 | ||||||||
\(255\) | −35.8534 | −2.24523 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.2646 | −1.32645 | −0.663223 | − | 0.748421i | \(-0.730812\pi\) | ||||
−0.663223 | + | 0.748421i | \(0.730812\pi\) | |||||||
\(258\) | −10.0491 | −0.625627 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.385456 | −0.0239050 | ||||||||
\(261\) | 4.63646 | 0.286990 | ||||||||
\(262\) | 14.2472 | 0.880198 | ||||||||
\(263\) | −29.5473 | −1.82197 | −0.910983 | − | 0.412445i | \(-0.864675\pi\) | ||||
−0.910983 | + | 0.412445i | \(0.864675\pi\) | |||||||
\(264\) | 13.1633 | 0.810145 | ||||||||
\(265\) | −17.7377 | −1.08962 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −28.1647 | −1.72365 | ||||||||
\(268\) | 14.7906 | 0.903477 | ||||||||
\(269\) | 7.45354 | 0.454450 | 0.227225 | − | 0.973842i | \(-0.427035\pi\) | ||||
0.227225 | + | 0.973842i | \(0.427035\pi\) | |||||||
\(270\) | 11.1979 | 0.681484 | ||||||||
\(271\) | −10.1490 | −0.616508 | −0.308254 | − | 0.951304i | \(-0.599745\pi\) | ||||
−0.308254 | + | 0.951304i | \(0.599745\pi\) | |||||||
\(272\) | −5.23961 | −0.317698 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.8382 | 0.715169 | ||||||||
\(275\) | 5.39006 | 0.325033 | ||||||||
\(276\) | 1.52683 | 0.0919044 | ||||||||
\(277\) | 4.36437 | 0.262230 | 0.131115 | − | 0.991367i | \(-0.458144\pi\) | ||||
0.131115 | + | 0.991367i | \(0.458144\pi\) | |||||||
\(278\) | −3.31290 | −0.198695 | ||||||||
\(279\) | −34.5440 | −2.06810 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0802 | 1.07857 | 0.539287 | − | 0.842122i | \(-0.318694\pi\) | ||||
0.539287 | + | 0.842122i | \(0.318694\pi\) | |||||||
\(282\) | −12.5889 | −0.749656 | ||||||||
\(283\) | 31.3250 | 1.86208 | 0.931039 | − | 0.364919i | \(-0.118903\pi\) | ||||
0.931039 | + | 0.364919i | \(0.118903\pi\) | |||||||
\(284\) | 13.6154 | 0.807924 | ||||||||
\(285\) | −9.90479 | −0.586709 | ||||||||
\(286\) | −0.741495 | −0.0438455 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.63646 | 0.273206 | ||||||||
\(289\) | 10.4535 | 0.614914 | ||||||||
\(290\) | 2.47620 | 0.145407 | ||||||||
\(291\) | 12.8918 | 0.755732 | ||||||||
\(292\) | 0.439855 | 0.0257406 | ||||||||
\(293\) | 6.80642 | 0.397635 | 0.198818 | − | 0.980037i | \(-0.436290\pi\) | ||||
0.198818 | + | 0.980037i | \(0.436290\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.9940 | −0.872982 | ||||||||
\(296\) | −8.07935 | −0.469602 | ||||||||
\(297\) | 21.5413 | 1.24995 | ||||||||
\(298\) | 11.7377 | 0.679948 | ||||||||
\(299\) | −0.0860072 | −0.00497392 | ||||||||
\(300\) | 3.12695 | 0.180535 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 21.5110 | 1.23782 | ||||||||
\(303\) | 23.2124 | 1.33351 | ||||||||
\(304\) | −1.44748 | −0.0830189 | ||||||||
\(305\) | 22.6001 | 1.29408 | ||||||||
\(306\) | −24.2933 | −1.38875 | ||||||||
\(307\) | 1.39528 | 0.0796327 | 0.0398163 | − | 0.999207i | \(-0.487323\pi\) | ||||
0.0398163 | + | 0.999207i | \(0.487323\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.1869 | 2.00171 | ||||||||
\(310\) | −18.4489 | −1.04783 | ||||||||
\(311\) | −14.8178 | −0.840241 | −0.420121 | − | 0.907468i | \(-0.638012\pi\) | ||||
−0.420121 | + | 0.907468i | \(0.638012\pi\) | |||||||
\(312\) | −0.430166 | −0.0243534 | ||||||||
\(313\) | 1.41720 | 0.0801047 | 0.0400524 | − | 0.999198i | \(-0.487248\pi\) | ||||
0.0400524 | + | 0.999198i | \(0.487248\pi\) | |||||||
\(314\) | 22.2380 | 1.25497 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.0107 | −0.956924 | ||||||||
\(317\) | 12.7045 | 0.713558 | 0.356779 | − | 0.934189i | \(-0.383875\pi\) | ||||
0.356779 | + | 0.934189i | \(0.383875\pi\) | |||||||
\(318\) | −19.7952 | −1.11006 | ||||||||
\(319\) | 4.76342 | 0.266700 | ||||||||
\(320\) | 2.47620 | 0.138424 | ||||||||
\(321\) | 3.78073 | 0.211020 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.58426 | 0.421999 | ||||||||
\(324\) | −1.41260 | −0.0784775 | ||||||||
\(325\) | −0.176143 | −0.00977064 | ||||||||
\(326\) | −18.4489 | −1.02179 | ||||||||
\(327\) | 23.5759 | 1.30375 | ||||||||
\(328\) | −4.66518 | −0.257591 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 32.5949 | 1.79429 | ||||||||
\(331\) | −20.4362 | −1.12328 | −0.561638 | − | 0.827383i | \(-0.689829\pi\) | ||||
−0.561638 | + | 0.827383i | \(0.689829\pi\) | |||||||
\(332\) | −6.10346 | −0.334971 | ||||||||
\(333\) | −37.4596 | −2.05277 | ||||||||
\(334\) | 21.5995 | 1.18187 | ||||||||
\(335\) | 36.6243 | 2.00100 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.35893 | −0.509814 | −0.254907 | − | 0.966966i | \(-0.582045\pi\) | ||||
−0.254907 | + | 0.966966i | \(0.582045\pi\) | |||||||
\(338\) | −12.9758 | −0.705789 | ||||||||
\(339\) | −38.7045 | −2.10214 | ||||||||
\(340\) | −12.9743 | −0.703631 | ||||||||
\(341\) | −35.4899 | −1.92188 | ||||||||
\(342\) | −6.71121 | −0.362901 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.63646 | −0.196065 | ||||||||
\(345\) | 3.78073 | 0.203548 | ||||||||
\(346\) | 1.04980 | 0.0564374 | ||||||||
\(347\) | −16.3113 | −0.875638 | −0.437819 | − | 0.899063i | \(-0.644249\pi\) | ||||
−0.437819 | + | 0.899063i | \(0.644249\pi\) | |||||||
\(348\) | 2.76342 | 0.148135 | ||||||||
\(349\) | 26.2630 | 1.40583 | 0.702913 | − | 0.711276i | \(-0.251882\pi\) | ||||
0.702913 | + | 0.711276i | \(0.251882\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.703951 | −0.0375741 | ||||||||
\(352\) | 4.76342 | 0.253891 | ||||||||
\(353\) | −8.89497 | −0.473431 | −0.236716 | − | 0.971579i | \(-0.576071\pi\) | ||||
−0.236716 | + | 0.971579i | \(0.576071\pi\) | |||||||
\(354\) | −16.7331 | −0.889356 | ||||||||
\(355\) | 33.7144 | 1.78937 | ||||||||
\(356\) | −10.1920 | −0.540175 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.1587 | 1.06542 | ||||||||
\(359\) | 1.88431 | 0.0994501 | 0.0497251 | − | 0.998763i | \(-0.484165\pi\) | ||||
0.0497251 | + | 0.998763i | \(0.484165\pi\) | |||||||
\(360\) | 11.4808 | 0.605091 | ||||||||
\(361\) | −16.9048 | −0.889726 | ||||||||
\(362\) | −0.155665 | −0.00818155 | ||||||||
\(363\) | 32.3047 | 1.69556 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.08917 | 0.0570096 | ||||||||
\(366\) | 25.2216 | 1.31835 | ||||||||
\(367\) | 19.0870 | 0.996332 | 0.498166 | − | 0.867082i | \(-0.334007\pi\) | ||||
0.498166 | + | 0.867082i | \(0.334007\pi\) | |||||||
\(368\) | 0.552516 | 0.0288019 | ||||||||
\(369\) | −21.6299 | −1.12601 | ||||||||
\(370\) | −20.0061 | −1.04007 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −20.5889 | −1.06748 | ||||||||
\(373\) | 14.4423 | 0.747793 | 0.373896 | − | 0.927470i | \(-0.378022\pi\) | ||||
0.373896 | + | 0.927470i | \(0.378022\pi\) | |||||||
\(374\) | −24.9585 | −1.29057 | ||||||||
\(375\) | −26.4709 | −1.36695 | ||||||||
\(376\) | −4.55554 | −0.234934 | ||||||||
\(377\) | −0.155665 | −0.00801714 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.4847 | 0.692661 | 0.346330 | − | 0.938113i | \(-0.387428\pi\) | ||||
0.346330 | + | 0.938113i | \(0.387428\pi\) | |||||||
\(380\) | −3.58426 | −0.183868 | ||||||||
\(381\) | 51.0658 | 2.61618 | ||||||||
\(382\) | −8.73313 | −0.446826 | ||||||||
\(383\) | 3.57820 | 0.182838 | 0.0914188 | − | 0.995813i | \(-0.470860\pi\) | ||||
0.0914188 | + | 0.995813i | \(0.470860\pi\) | |||||||
\(384\) | 2.76342 | 0.141020 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.742332 | −0.0377837 | ||||||||
\(387\) | −16.8603 | −0.857059 | ||||||||
\(388\) | 4.66518 | 0.236838 | ||||||||
\(389\) | −6.55252 | −0.332226 | −0.166113 | − | 0.986107i | \(-0.553122\pi\) | ||||
−0.166113 | + | 0.986107i | \(0.553122\pi\) | |||||||
\(390\) | −1.06518 | −0.0539373 | ||||||||
\(391\) | −2.89497 | −0.146405 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 39.3710 | 1.98601 | ||||||||
\(394\) | −10.2692 | −0.517353 | ||||||||
\(395\) | −42.1217 | −2.11937 | ||||||||
\(396\) | 22.0854 | 1.10983 | ||||||||
\(397\) | 31.0751 | 1.55961 | 0.779807 | − | 0.626020i | \(-0.215317\pi\) | ||||
0.779807 | + | 0.626020i | \(0.215317\pi\) | |||||||
\(398\) | −0.574436 | −0.0287939 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.13155 | 0.0565777 | ||||||||
\(401\) | −25.8678 | −1.29178 | −0.645889 | − | 0.763431i | \(-0.723513\pi\) | ||||
−0.645889 | + | 0.763431i | \(0.723513\pi\) | |||||||
\(402\) | 40.8724 | 2.03853 | ||||||||
\(403\) | 1.15978 | 0.0577728 | ||||||||
\(404\) | 8.39988 | 0.417910 | ||||||||
\(405\) | −3.49787 | −0.173810 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −38.4853 | −1.90764 | ||||||||
\(408\) | −14.4792 | −0.716828 | ||||||||
\(409\) | 1.61152 | 0.0796843 | 0.0398422 | − | 0.999206i | \(-0.487314\pi\) | ||||
0.0398422 | + | 0.999206i | \(0.487314\pi\) | |||||||
\(410\) | −11.5519 | −0.570508 | ||||||||
\(411\) | 32.7138 | 1.61365 | ||||||||
\(412\) | 12.7331 | 0.627316 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.56172 | 0.125902 | ||||||||
\(415\) | −15.1134 | −0.741886 | ||||||||
\(416\) | −0.155665 | −0.00763209 | ||||||||
\(417\) | −9.15493 | −0.448319 | ||||||||
\(418\) | −6.89497 | −0.337244 | ||||||||
\(419\) | 3.62423 | 0.177055 | 0.0885277 | − | 0.996074i | \(-0.471784\pi\) | ||||
0.0885277 | + | 0.996074i | \(0.471784\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0280 | 0.488734 | 0.244367 | − | 0.969683i | \(-0.421420\pi\) | ||||
0.244367 | + | 0.969683i | \(0.421420\pi\) | |||||||
\(422\) | −13.4264 | −0.653587 | ||||||||
\(423\) | −21.1216 | −1.02697 | ||||||||
\(424\) | −7.16329 | −0.347880 | ||||||||
\(425\) | −5.92890 | −0.287594 | ||||||||
\(426\) | 37.6249 | 1.82293 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.36814 | 0.0661314 | ||||||||
\(429\) | −2.04906 | −0.0989295 | ||||||||
\(430\) | −9.00460 | −0.434240 | ||||||||
\(431\) | 3.57987 | 0.172436 | 0.0862182 | − | 0.996276i | \(-0.472522\pi\) | ||||
0.0862182 | + | 0.996276i | \(0.472522\pi\) | |||||||
\(432\) | 4.52223 | 0.217576 | ||||||||
\(433\) | 12.5125 | 0.601314 | 0.300657 | − | 0.953732i | \(-0.402794\pi\) | ||||
0.300657 | + | 0.953732i | \(0.402794\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.84276 | 0.328085 | ||||||||
\(436\) | 8.53143 | 0.408582 | ||||||||
\(437\) | −0.799758 | −0.0382576 | ||||||||
\(438\) | 1.21550 | 0.0580789 | ||||||||
\(439\) | −22.7906 | −1.08773 | −0.543867 | − | 0.839171i | \(-0.683040\pi\) | ||||
−0.543867 | + | 0.839171i | \(0.683040\pi\) | |||||||
\(440\) | 11.7952 | 0.562312 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.815622 | 0.0387952 | ||||||||
\(443\) | 25.6636 | 1.21931 | 0.609657 | − | 0.792665i | \(-0.291307\pi\) | ||||
0.609657 | + | 0.792665i | \(0.291307\pi\) | |||||||
\(444\) | −22.3266 | −1.05957 | ||||||||
\(445\) | −25.2374 | −1.19637 | ||||||||
\(446\) | −5.67947 | −0.268931 | ||||||||
\(447\) | 32.4362 | 1.53418 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.07269 | −0.286588 | −0.143294 | − | 0.989680i | \(-0.545769\pi\) | ||||
−0.143294 | + | 0.989680i | \(0.545769\pi\) | |||||||
\(450\) | 5.24641 | 0.247318 | ||||||||
\(451\) | −22.2222 | −1.04640 | ||||||||
\(452\) | −14.0061 | −0.658789 | ||||||||
\(453\) | 59.4437 | 2.79291 | ||||||||
\(454\) | 20.9124 | 0.981468 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.00000 | −0.187317 | ||||||||
\(457\) | 12.3485 | 0.577639 | 0.288819 | − | 0.957384i | \(-0.406737\pi\) | ||||
0.288819 | + | 0.957384i | \(0.406737\pi\) | |||||||
\(458\) | −22.6598 | −1.05882 | ||||||||
\(459\) | −23.6947 | −1.10598 | ||||||||
\(460\) | 1.36814 | 0.0637898 | ||||||||
\(461\) | 32.6024 | 1.51845 | 0.759223 | − | 0.650831i | \(-0.225579\pi\) | ||||
0.759223 | + | 0.650831i | \(0.225579\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.73023 | 0.452202 | 0.226101 | − | 0.974104i | \(-0.427402\pi\) | ||||
0.226101 | + | 0.974104i | \(0.427402\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | −50.9821 | −2.36424 | ||||||||
\(466\) | 18.9002 | 0.875534 | ||||||||
\(467\) | 33.0234 | 1.52814 | 0.764070 | − | 0.645134i | \(-0.223198\pi\) | ||||
0.764070 | + | 0.645134i | \(0.223198\pi\) | |||||||
\(468\) | −0.721733 | −0.0333621 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −11.2804 | −0.520327 | ||||||||
\(471\) | 61.4529 | 2.83160 | ||||||||
\(472\) | −6.05523 | −0.278715 | ||||||||
\(473\) | −17.3220 | −0.796466 | ||||||||
\(474\) | −47.0075 | −2.15913 | ||||||||
\(475\) | −1.63791 | −0.0751523 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −33.2124 | −1.52069 | ||||||||
\(478\) | −24.4945 | −1.12035 | ||||||||
\(479\) | −5.96752 | −0.272663 | −0.136332 | − | 0.990663i | \(-0.543531\pi\) | ||||
−0.136332 | + | 0.990663i | \(0.543531\pi\) | |||||||
\(480\) | 6.84276 | 0.312328 | ||||||||
\(481\) | 1.25767 | 0.0573447 | ||||||||
\(482\) | 29.2268 | 1.33124 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.6901 | 0.531369 | ||||||||
\(485\) | 11.5519 | 0.524545 | ||||||||
\(486\) | −17.4703 | −0.792468 | ||||||||
\(487\) | 22.4126 | 1.01561 | 0.507806 | − | 0.861472i | \(-0.330457\pi\) | ||||
0.507806 | + | 0.861472i | \(0.330457\pi\) | |||||||
\(488\) | 9.12695 | 0.413158 | ||||||||
\(489\) | −50.9821 | −2.30549 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.5949 | 0.568401 | 0.284200 | − | 0.958765i | \(-0.408272\pi\) | ||||
0.284200 | + | 0.958765i | \(0.408272\pi\) | |||||||
\(492\) | −12.8918 | −0.581208 | ||||||||
\(493\) | −5.23961 | −0.235980 | ||||||||
\(494\) | 0.225322 | 0.0101377 | ||||||||
\(495\) | 54.6878 | 2.45803 | ||||||||
\(496\) | −7.45051 | −0.334538 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −16.8664 | −0.755801 | ||||||||
\(499\) | −39.7490 | −1.77941 | −0.889705 | − | 0.456536i | \(-0.849090\pi\) | ||||
−0.889705 | + | 0.456536i | \(0.849090\pi\) | |||||||
\(500\) | −9.57904 | −0.428388 | ||||||||
\(501\) | 59.6884 | 2.66668 | ||||||||
\(502\) | −6.45209 | −0.287971 | ||||||||
\(503\) | −0.561599 | −0.0250405 | −0.0125202 | − | 0.999922i | \(-0.503985\pi\) | ||||
−0.0125202 | + | 0.999922i | \(0.503985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.7998 | 0.925577 | ||||||||
\(506\) | 2.63186 | 0.117001 | ||||||||
\(507\) | −35.8574 | −1.59248 | ||||||||
\(508\) | 18.4792 | 0.819883 | ||||||||
\(509\) | −39.8126 | −1.76466 | −0.882331 | − | 0.470629i | \(-0.844027\pi\) | ||||
−0.882331 | + | 0.470629i | \(0.844027\pi\) | |||||||
\(510\) | −35.8534 | −1.58762 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.54585 | −0.289007 | ||||||||
\(514\) | −21.2646 | −0.937940 | ||||||||
\(515\) | 31.5297 | 1.38937 | ||||||||
\(516\) | −10.0491 | −0.442385 | ||||||||
\(517\) | −21.6999 | −0.954363 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.90102 | 0.127341 | ||||||||
\(520\) | −0.385456 | −0.0169034 | ||||||||
\(521\) | −12.2017 | −0.534566 | −0.267283 | − | 0.963618i | \(-0.586126\pi\) | ||||
−0.267283 | + | 0.963618i | \(0.586126\pi\) | |||||||
\(522\) | 4.63646 | 0.202933 | ||||||||
\(523\) | −14.8305 | −0.648494 | −0.324247 | − | 0.945972i | \(-0.605111\pi\) | ||||
−0.324247 | + | 0.945972i | \(0.605111\pi\) | |||||||
\(524\) | 14.2472 | 0.622394 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29.5473 | −1.28832 | ||||||||
\(527\) | 39.0378 | 1.70051 | ||||||||
\(528\) | 13.1633 | 0.572859 | ||||||||
\(529\) | −22.6947 | −0.986727 | ||||||||
\(530\) | −17.7377 | −0.770478 | ||||||||
\(531\) | −28.0749 | −1.21835 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.726203 | 0.0314553 | ||||||||
\(534\) | −28.1647 | −1.21881 | ||||||||
\(535\) | 3.38778 | 0.146466 | ||||||||
\(536\) | 14.7906 | 0.638855 | ||||||||
\(537\) | 55.7068 | 2.40393 | ||||||||
\(538\) | 7.45354 | 0.321345 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 11.1979 | 0.481882 | ||||||||
\(541\) | −0.588022 | −0.0252810 | −0.0126405 | − | 0.999920i | \(-0.504024\pi\) | ||||
−0.0126405 | + | 0.999920i | \(0.504024\pi\) | |||||||
\(542\) | −10.1490 | −0.435937 | ||||||||
\(543\) | −0.430166 | −0.0184602 | ||||||||
\(544\) | −5.23961 | −0.224647 | ||||||||
\(545\) | 21.1255 | 0.904917 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.0159 | 0.813060 | 0.406530 | − | 0.913637i | \(-0.366739\pi\) | ||||
0.406530 | + | 0.913637i | \(0.366739\pi\) | |||||||
\(548\) | 11.8382 | 0.505701 | ||||||||
\(549\) | 42.3168 | 1.80604 | ||||||||
\(550\) | 5.39006 | 0.229833 | ||||||||
\(551\) | −1.44748 | −0.0616649 | ||||||||
\(552\) | 1.52683 | 0.0649862 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.36437 | 0.185424 | ||||||||
\(555\) | −55.2850 | −2.34672 | ||||||||
\(556\) | −3.31290 | −0.140498 | ||||||||
\(557\) | 0.253903 | 0.0107582 | 0.00537911 | − | 0.999986i | \(-0.498288\pi\) | ||||
0.00537911 | + | 0.999986i | \(0.498288\pi\) | |||||||
\(558\) | −34.5440 | −1.46237 | ||||||||
\(559\) | 0.566069 | 0.0239422 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −68.9706 | −2.91194 | ||||||||
\(562\) | 18.0802 | 0.762666 | ||||||||
\(563\) | −29.1094 | −1.22681 | −0.613407 | − | 0.789767i | \(-0.710201\pi\) | ||||
−0.613407 | + | 0.789767i | \(0.710201\pi\) | |||||||
\(564\) | −12.5889 | −0.530087 | ||||||||
\(565\) | −34.6818 | −1.45907 | ||||||||
\(566\) | 31.3250 | 1.31669 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.6154 | 0.571289 | ||||||||
\(569\) | −37.7068 | −1.58075 | −0.790376 | − | 0.612621i | \(-0.790115\pi\) | ||||
−0.790376 | + | 0.612621i | \(0.790115\pi\) | |||||||
\(570\) | −9.90479 | −0.414866 | ||||||||
\(571\) | 32.3418 | 1.35346 | 0.676732 | − | 0.736229i | \(-0.263396\pi\) | ||||
0.676732 | + | 0.736229i | \(0.263396\pi\) | |||||||
\(572\) | −0.741495 | −0.0310035 | ||||||||
\(573\) | −24.1333 | −1.00818 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.625201 | 0.0260727 | ||||||||
\(576\) | 4.63646 | 0.193186 | ||||||||
\(577\) | 10.1438 | 0.422291 | 0.211146 | − | 0.977455i | \(-0.432281\pi\) | ||||
0.211146 | + | 0.977455i | \(0.432281\pi\) | |||||||
\(578\) | 10.4535 | 0.434810 | ||||||||
\(579\) | −2.05137 | −0.0852521 | ||||||||
\(580\) | 2.47620 | 0.102818 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 12.8918 | 0.534383 | ||||||||
\(583\) | −34.1217 | −1.41318 | ||||||||
\(584\) | 0.439855 | 0.0182013 | ||||||||
\(585\) | −1.78715 | −0.0738897 | ||||||||
\(586\) | 6.80642 | 0.281171 | ||||||||
\(587\) | −26.4453 | −1.09151 | −0.545757 | − | 0.837943i | \(-0.683758\pi\) | ||||
−0.545757 | + | 0.837943i | \(0.683758\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.7845 | 0.444368 | ||||||||
\(590\) | −14.9940 | −0.617291 | ||||||||
\(591\) | −28.3780 | −1.16731 | ||||||||
\(592\) | −8.07935 | −0.332059 | ||||||||
\(593\) | 5.83900 | 0.239779 | 0.119889 | − | 0.992787i | \(-0.461746\pi\) | ||||
0.119889 | + | 0.992787i | \(0.461746\pi\) | |||||||
\(594\) | 21.5413 | 0.883848 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.7377 | 0.480796 | ||||||||
\(597\) | −1.58740 | −0.0649681 | ||||||||
\(598\) | −0.0860072 | −0.00351709 | ||||||||
\(599\) | −10.1157 | −0.413316 | −0.206658 | − | 0.978413i | \(-0.566259\pi\) | ||||
−0.206658 | + | 0.978413i | \(0.566259\pi\) | |||||||
\(600\) | 3.12695 | 0.127657 | ||||||||
\(601\) | −34.5954 | −1.41118 | −0.705588 | − | 0.708622i | \(-0.749317\pi\) | ||||
−0.705588 | + | 0.708622i | \(0.749317\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 68.5759 | 2.79263 | ||||||||
\(604\) | 21.5110 | 0.875269 | ||||||||
\(605\) | 28.9471 | 1.17687 | ||||||||
\(606\) | 23.2124 | 0.942937 | ||||||||
\(607\) | −10.8339 | −0.439735 | −0.219867 | − | 0.975530i | \(-0.570562\pi\) | ||||
−0.219867 | + | 0.975530i | \(0.570562\pi\) | |||||||
\(608\) | −1.44748 | −0.0587032 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.6001 | 0.915053 | ||||||||
\(611\) | 0.709137 | 0.0286886 | ||||||||
\(612\) | −24.2933 | −0.981997 | ||||||||
\(613\) | 6.67487 | 0.269595 | 0.134798 | − | 0.990873i | \(-0.456962\pi\) | ||||
0.134798 | + | 0.990873i | \(0.456962\pi\) | |||||||
\(614\) | 1.39528 | 0.0563088 | ||||||||
\(615\) | −31.9227 | −1.28725 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.7039 | 0.471182 | 0.235591 | − | 0.971852i | \(-0.424297\pi\) | ||||
0.235591 | + | 0.971852i | \(0.424297\pi\) | |||||||
\(618\) | 35.1869 | 1.41543 | ||||||||
\(619\) | −28.2525 | −1.13556 | −0.567781 | − | 0.823180i | \(-0.692198\pi\) | ||||
−0.567781 | + | 0.823180i | \(0.692198\pi\) | |||||||
\(620\) | −18.4489 | −0.740927 | ||||||||
\(621\) | 2.49860 | 0.100265 | ||||||||
\(622\) | −14.8178 | −0.594140 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.430166 | −0.0172204 | ||||||||
\(625\) | −29.3774 | −1.17509 | ||||||||
\(626\) | 1.41720 | 0.0566426 | ||||||||
\(627\) | −19.0537 | −0.760930 | ||||||||
\(628\) | 22.2380 | 0.887394 | ||||||||
\(629\) | 42.3326 | 1.68791 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.3197 | −1.80415 | −0.902074 | − | 0.431582i | \(-0.857956\pi\) | ||||
−0.902074 | + | 0.431582i | \(0.857956\pi\) | |||||||
\(632\) | −17.0107 | −0.676648 | ||||||||
\(633\) | −37.1027 | −1.47470 | ||||||||
\(634\) | 12.7045 | 0.504562 | ||||||||
\(635\) | 45.7582 | 1.81586 | ||||||||
\(636\) | −19.7952 | −0.784929 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.76342 | 0.188585 | ||||||||
\(639\) | 63.1272 | 2.49727 | ||||||||
\(640\) | 2.47620 | 0.0978803 | ||||||||
\(641\) | −9.38778 | −0.370795 | −0.185398 | − | 0.982664i | \(-0.559357\pi\) | ||||
−0.185398 | + | 0.982664i | \(0.559357\pi\) | |||||||
\(642\) | 3.78073 | 0.149214 | ||||||||
\(643\) | −17.5246 | −0.691104 | −0.345552 | − | 0.938400i | \(-0.612308\pi\) | ||||
−0.345552 | + | 0.938400i | \(0.612308\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.8835 | −0.979785 | ||||||||
\(646\) | 7.58426 | 0.298399 | ||||||||
\(647\) | 32.0603 | 1.26042 | 0.630211 | − | 0.776424i | \(-0.282968\pi\) | ||||
0.630211 | + | 0.776424i | \(0.282968\pi\) | |||||||
\(648\) | −1.41260 | −0.0554920 | ||||||||
\(649\) | −28.8436 | −1.13221 | ||||||||
\(650\) | −0.176143 | −0.00690889 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.4489 | −0.722516 | ||||||||
\(653\) | −17.5903 | −0.688362 | −0.344181 | − | 0.938903i | \(-0.611843\pi\) | ||||
−0.344181 | + | 0.938903i | \(0.611843\pi\) | |||||||
\(654\) | 23.5759 | 0.921890 | ||||||||
\(655\) | 35.2790 | 1.37846 | ||||||||
\(656\) | −4.66518 | −0.182145 | ||||||||
\(657\) | 2.03937 | 0.0795634 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.2902 | 0.868305 | 0.434152 | − | 0.900839i | \(-0.357048\pi\) | ||||
0.434152 | + | 0.900839i | \(0.357048\pi\) | |||||||
\(660\) | 32.5949 | 1.26876 | ||||||||
\(661\) | −24.3288 | −0.946280 | −0.473140 | − | 0.880987i | \(-0.656879\pi\) | ||||
−0.473140 | + | 0.880987i | \(0.656879\pi\) | |||||||
\(662\) | −20.4362 | −0.794276 | ||||||||
\(663\) | 2.25390 | 0.0875343 | ||||||||
\(664\) | −6.10346 | −0.236860 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −37.4596 | −1.45153 | ||||||||
\(667\) | 0.552516 | 0.0213935 | ||||||||
\(668\) | 21.5995 | 0.835710 | ||||||||
\(669\) | −15.6947 | −0.606793 | ||||||||
\(670\) | 36.6243 | 1.41492 | ||||||||
\(671\) | 43.4755 | 1.67835 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.97515 | −0.191778 | −0.0958890 | − | 0.995392i | \(-0.530569\pi\) | ||||
−0.0958890 | + | 0.995392i | \(0.530569\pi\) | |||||||
\(674\) | −9.35893 | −0.360493 | ||||||||
\(675\) | 5.11714 | 0.196959 | ||||||||
\(676\) | −12.9758 | −0.499068 | ||||||||
\(677\) | −12.7839 | −0.491325 | −0.245662 | − | 0.969355i | \(-0.579005\pi\) | ||||
−0.245662 | + | 0.969355i | \(0.579005\pi\) | |||||||
\(678\) | −38.7045 | −1.48644 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −12.9743 | −0.497542 | ||||||||
\(681\) | 57.7897 | 2.21451 | ||||||||
\(682\) | −35.4899 | −1.35898 | ||||||||
\(683\) | 25.1171 | 0.961081 | 0.480540 | − | 0.876973i | \(-0.340441\pi\) | ||||
0.480540 | + | 0.876973i | \(0.340441\pi\) | |||||||
\(684\) | −6.71121 | −0.256609 | ||||||||
\(685\) | 29.3136 | 1.12002 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −62.6185 | −2.38905 | ||||||||
\(688\) | −3.63646 | −0.138639 | ||||||||
\(689\) | 1.11507 | 0.0424808 | ||||||||
\(690\) | 3.78073 | 0.143930 | ||||||||
\(691\) | −50.0191 | −1.90282 | −0.951409 | − | 0.307931i | \(-0.900363\pi\) | ||||
−0.951409 | + | 0.307931i | \(0.900363\pi\) | |||||||
\(692\) | 1.04980 | 0.0399073 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.3113 | −0.619170 | ||||||||
\(695\) | −8.20340 | −0.311173 | ||||||||
\(696\) | 2.76342 | 0.104747 | ||||||||
\(697\) | 24.4437 | 0.925872 | ||||||||
\(698\) | 26.2630 | 0.994069 | ||||||||
\(699\) | 52.2291 | 1.97548 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.3165 | 0.767345 | 0.383673 | − | 0.923469i | \(-0.374659\pi\) | ||||
0.383673 | + | 0.923469i | \(0.374659\pi\) | |||||||
\(702\) | −0.703951 | −0.0265689 | ||||||||
\(703\) | 11.6947 | 0.441075 | ||||||||
\(704\) | 4.76342 | 0.179528 | ||||||||
\(705\) | −31.1725 | −1.17402 | ||||||||
\(706\) | −8.89497 | −0.334767 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −16.7331 | −0.628869 | ||||||||
\(709\) | −26.0161 | −0.977055 | −0.488527 | − | 0.872549i | \(-0.662466\pi\) | ||||
−0.488527 | + | 0.872549i | \(0.662466\pi\) | |||||||
\(710\) | 33.7144 | 1.26528 | ||||||||
\(711\) | −78.8693 | −2.95783 | ||||||||
\(712\) | −10.1920 | −0.381962 | ||||||||
\(713\) | −4.11653 | −0.154165 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.83609 | −0.0686658 | ||||||||
\(716\) | 20.1587 | 0.753366 | ||||||||
\(717\) | −67.6884 | −2.52787 | ||||||||
\(718\) | 1.88431 | 0.0703219 | ||||||||
\(719\) | 18.5519 | 0.691870 | 0.345935 | − | 0.938259i | \(-0.387562\pi\) | ||||
0.345935 | + | 0.938259i | \(0.387562\pi\) | |||||||
\(720\) | 11.4808 | 0.427864 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −16.9048 | −0.629131 | ||||||||
\(723\) | 80.7657 | 3.00371 | ||||||||
\(724\) | −0.155665 | −0.00578523 | ||||||||
\(725\) | 1.13155 | 0.0420248 | ||||||||
\(726\) | 32.3047 | 1.19894 | ||||||||
\(727\) | −1.02788 | −0.0381218 | −0.0190609 | − | 0.999818i | \(-0.506068\pi\) | ||||
−0.0190609 | + | 0.999818i | \(0.506068\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −44.0398 | −1.63110 | ||||||||
\(730\) | 1.08917 | 0.0403119 | ||||||||
\(731\) | 19.0537 | 0.704725 | ||||||||
\(732\) | 25.2216 | 0.932216 | ||||||||
\(733\) | 19.8632 | 0.733665 | 0.366833 | − | 0.930287i | \(-0.380442\pi\) | ||||
0.366833 | + | 0.930287i | \(0.380442\pi\) | |||||||
\(734\) | 19.0870 | 0.704513 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.552516 | 0.0203660 | ||||||||
\(737\) | 70.4536 | 2.59519 | ||||||||
\(738\) | −21.6299 | −0.796208 | ||||||||
\(739\) | −18.9094 | −0.695593 | −0.347797 | − | 0.937570i | \(-0.613070\pi\) | ||||
−0.347797 | + | 0.937570i | \(0.613070\pi\) | |||||||
\(740\) | −20.0061 | −0.735437 | ||||||||
\(741\) | 0.622658 | 0.0228739 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.5078 | −0.605613 | −0.302806 | − | 0.953052i | \(-0.597924\pi\) | ||||
−0.302806 | + | 0.953052i | \(0.597924\pi\) | |||||||
\(744\) | −20.5889 | −0.754824 | ||||||||
\(745\) | 29.0649 | 1.06486 | ||||||||
\(746\) | 14.4423 | 0.528769 | ||||||||
\(747\) | −28.2985 | −1.03539 | ||||||||
\(748\) | −24.9585 | −0.912571 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −26.4709 | −0.966579 | ||||||||
\(751\) | −29.1610 | −1.06410 | −0.532050 | − | 0.846713i | \(-0.678578\pi\) | ||||
−0.532050 | + | 0.846713i | \(0.678578\pi\) | |||||||
\(752\) | −4.55554 | −0.166124 | ||||||||
\(753\) | −17.8298 | −0.649754 | ||||||||
\(754\) | −0.155665 | −0.00566897 | ||||||||
\(755\) | 53.2654 | 1.93853 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.9956 | 1.34463 | 0.672315 | − | 0.740266i | \(-0.265300\pi\) | ||||
0.672315 | + | 0.740266i | \(0.265300\pi\) | |||||||
\(758\) | 13.4847 | 0.489785 | ||||||||
\(759\) | 7.27293 | 0.263991 | ||||||||
\(760\) | −3.58426 | −0.130015 | ||||||||
\(761\) | −47.1171 | −1.70800 | −0.853998 | − | 0.520277i | \(-0.825829\pi\) | ||||
−0.853998 | + | 0.520277i | \(0.825829\pi\) | |||||||
\(762\) | 51.0658 | 1.84992 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.73313 | −0.315953 | ||||||||
\(765\) | −60.1549 | −2.17491 | ||||||||
\(766\) | 3.57820 | 0.129286 | ||||||||
\(767\) | 0.942586 | 0.0340348 | ||||||||
\(768\) | 2.76342 | 0.0997162 | ||||||||
\(769\) | −6.52174 | −0.235180 | −0.117590 | − | 0.993062i | \(-0.537517\pi\) | ||||
−0.117590 | + | 0.993062i | \(0.537517\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −58.7628 | −2.11629 | ||||||||
\(772\) | −0.742332 | −0.0267171 | ||||||||
\(773\) | 16.3332 | 0.587466 | 0.293733 | − | 0.955887i | \(-0.405102\pi\) | ||||
0.293733 | + | 0.955887i | \(0.405102\pi\) | |||||||
\(774\) | −16.8603 | −0.606032 | ||||||||
\(775\) | −8.43065 | −0.302838 | ||||||||
\(776\) | 4.66518 | 0.167470 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.55252 | −0.234919 | ||||||||
\(779\) | 6.75277 | 0.241943 | ||||||||
\(780\) | −1.06518 | −0.0381394 | ||||||||
\(781\) | 64.8557 | 2.32072 | ||||||||
\(782\) | −2.89497 | −0.103524 | ||||||||
\(783\) | 4.52223 | 0.161611 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 55.0658 | 1.96538 | ||||||||
\(786\) | 39.3710 | 1.40432 | ||||||||
\(787\) | −38.0673 | −1.35695 | −0.678477 | − | 0.734621i | \(-0.737360\pi\) | ||||
−0.678477 | + | 0.734621i | \(0.737360\pi\) | |||||||
\(788\) | −10.2692 | −0.365824 | ||||||||
\(789\) | −81.6515 | −2.90687 | ||||||||
\(790\) | −42.1217 | −1.49862 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 22.0854 | 0.784771 | ||||||||
\(793\) | −1.42074 | −0.0504521 | ||||||||
\(794\) | 31.0751 | 1.10281 | ||||||||
\(795\) | −49.0167 | −1.73844 | ||||||||
\(796\) | −0.574436 | −0.0203603 | ||||||||
\(797\) | −35.7665 | −1.26692 | −0.633458 | − | 0.773777i | \(-0.718365\pi\) | ||||
−0.633458 | + | 0.773777i | \(0.718365\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.8693 | 0.844435 | ||||||||
\(800\) | 1.13155 | 0.0400064 | ||||||||
\(801\) | −47.2549 | −1.66967 | ||||||||
\(802\) | −25.8678 | −0.913425 | ||||||||
\(803\) | 2.09521 | 0.0739384 | ||||||||
\(804\) | 40.8724 | 1.44146 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.15978 | 0.0408515 | ||||||||
\(807\) | 20.5972 | 0.725057 | ||||||||
\(808\) | 8.39988 | 0.295507 | ||||||||
\(809\) | 7.33035 | 0.257722 | 0.128861 | − | 0.991663i | \(-0.458868\pi\) | ||||
0.128861 | + | 0.991663i | \(0.458868\pi\) | |||||||
\(810\) | −3.49787 | −0.122902 | ||||||||
\(811\) | −25.1377 | −0.882705 | −0.441353 | − | 0.897334i | \(-0.645501\pi\) | ||||
−0.441353 | + | 0.897334i | \(0.645501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.0459 | −0.983613 | ||||||||
\(814\) | −38.4853 | −1.34891 | ||||||||
\(815\) | −45.6832 | −1.60021 | ||||||||
\(816\) | −14.4792 | −0.506874 | ||||||||
\(817\) | 5.26372 | 0.184154 | ||||||||
\(818\) | 1.61152 | 0.0563453 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.5519 | −0.403410 | ||||||||
\(821\) | 12.5857 | 0.439244 | 0.219622 | − | 0.975585i | \(-0.429518\pi\) | ||||
0.219622 | + | 0.975585i | \(0.429518\pi\) | |||||||
\(822\) | 32.7138 | 1.14102 | ||||||||
\(823\) | 5.08662 | 0.177309 | 0.0886543 | − | 0.996062i | \(-0.471743\pi\) | ||||
0.0886543 | + | 0.996062i | \(0.471743\pi\) | |||||||
\(824\) | 12.7331 | 0.443580 | ||||||||
\(825\) | 14.8950 | 0.518576 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.9244 | 1.17967 | 0.589833 | − | 0.807525i | \(-0.299193\pi\) | ||||
0.589833 | + | 0.807525i | \(0.299193\pi\) | |||||||
\(828\) | 2.56172 | 0.0890259 | ||||||||
\(829\) | 36.0762 | 1.25298 | 0.626489 | − | 0.779430i | \(-0.284491\pi\) | ||||
0.626489 | + | 0.779430i | \(0.284491\pi\) | |||||||
\(830\) | −15.1134 | −0.524593 | ||||||||
\(831\) | 12.0606 | 0.418377 | ||||||||
\(832\) | −0.155665 | −0.00539670 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −9.15493 | −0.317009 | ||||||||
\(835\) | 53.4847 | 1.85091 | ||||||||
\(836\) | −6.89497 | −0.238467 | ||||||||
\(837\) | −33.6929 | −1.16460 | ||||||||
\(838\) | 3.62423 | 0.125197 | ||||||||
\(839\) | −29.0983 | −1.00458 | −0.502292 | − | 0.864698i | \(-0.667510\pi\) | ||||
−0.502292 | + | 0.864698i | \(0.667510\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 10.0280 | 0.345587 | ||||||||
\(843\) | 49.9631 | 1.72082 | ||||||||
\(844\) | −13.4264 | −0.462156 | ||||||||
\(845\) | −32.1306 | −1.10532 | ||||||||
\(846\) | −21.1216 | −0.726176 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.16329 | −0.245989 | ||||||||
\(849\) | 86.5640 | 2.97087 | ||||||||
\(850\) | −5.92890 | −0.203360 | ||||||||
\(851\) | −4.46397 | −0.153023 | ||||||||
\(852\) | 37.6249 | 1.28901 | ||||||||
\(853\) | −10.9169 | −0.373787 | −0.186894 | − | 0.982380i | \(-0.559842\pi\) | ||||
−0.186894 | + | 0.982380i | \(0.559842\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.6183 | −0.568333 | ||||||||
\(856\) | 1.36814 | 0.0467620 | ||||||||
\(857\) | 31.7421 | 1.08429 | 0.542145 | − | 0.840285i | \(-0.317612\pi\) | ||||
0.542145 | + | 0.840285i | \(0.317612\pi\) | |||||||
\(858\) | −2.04906 | −0.0699537 | ||||||||
\(859\) | 11.5632 | 0.394530 | 0.197265 | − | 0.980350i | \(-0.436794\pi\) | ||||
0.197265 | + | 0.980350i | \(0.436794\pi\) | |||||||
\(860\) | −9.00460 | −0.307054 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.57987 | 0.121931 | ||||||||
\(863\) | −31.4596 | −1.07090 | −0.535449 | − | 0.844568i | \(-0.679857\pi\) | ||||
−0.535449 | + | 0.844568i | \(0.679857\pi\) | |||||||
\(864\) | 4.52223 | 0.153849 | ||||||||
\(865\) | 2.59950 | 0.0883858 | ||||||||
\(866\) | 12.5125 | 0.425193 | ||||||||
\(867\) | 28.8875 | 0.981070 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −81.0288 | −2.74871 | ||||||||
\(870\) | 6.84276 | 0.231991 | ||||||||
\(871\) | −2.30237 | −0.0780127 | ||||||||
\(872\) | 8.53143 | 0.288911 | ||||||||
\(873\) | 21.6299 | 0.732062 | ||||||||
\(874\) | −0.799758 | −0.0270522 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.21550 | 0.0410680 | ||||||||
\(877\) | −9.49715 | −0.320696 | −0.160348 | − | 0.987061i | \(-0.551262\pi\) | ||||
−0.160348 | + | 0.987061i | \(0.551262\pi\) | |||||||
\(878\) | −22.7906 | −0.769144 | ||||||||
\(879\) | 18.8090 | 0.634411 | ||||||||
\(880\) | 11.7952 | 0.397615 | ||||||||
\(881\) | 33.2641 | 1.12070 | 0.560348 | − | 0.828258i | \(-0.310668\pi\) | ||||
0.560348 | + | 0.828258i | \(0.310668\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.5805 | 0.961810 | 0.480905 | − | 0.876773i | \(-0.340308\pi\) | ||||
0.480905 | + | 0.876773i | \(0.340308\pi\) | |||||||
\(884\) | 0.815622 | 0.0274323 | ||||||||
\(885\) | −41.4345 | −1.39281 | ||||||||
\(886\) | 25.6636 | 0.862186 | ||||||||
\(887\) | 17.5397 | 0.588924 | 0.294462 | − | 0.955663i | \(-0.404859\pi\) | ||||
0.294462 | + | 0.955663i | \(0.404859\pi\) | |||||||
\(888\) | −22.3266 | −0.749231 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −25.2374 | −0.845960 | ||||||||
\(891\) | −6.72878 | −0.225423 | ||||||||
\(892\) | −5.67947 | −0.190163 | ||||||||
\(893\) | 6.59408 | 0.220662 | ||||||||
\(894\) | 32.4362 | 1.08483 | ||||||||
\(895\) | 49.9169 | 1.66854 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.237673 | −0.00793569 | ||||||||
\(898\) | −6.07269 | −0.202648 | ||||||||
\(899\) | −7.45051 | −0.248488 | ||||||||
\(900\) | 5.24641 | 0.174880 | ||||||||
\(901\) | 37.5329 | 1.25040 | ||||||||
\(902\) | −22.2222 | −0.739917 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.0061 | −0.465834 | ||||||||
\(905\) | −0.385456 | −0.0128130 | ||||||||
\(906\) | 59.4437 | 1.97489 | ||||||||
\(907\) | −13.1558 | −0.436831 | −0.218416 | − | 0.975856i | \(-0.570089\pi\) | ||||
−0.218416 | + | 0.975856i | \(0.570089\pi\) | |||||||
\(908\) | 20.9124 | 0.694003 | ||||||||
\(909\) | 38.9457 | 1.29175 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.5797 | −0.880623 | −0.440312 | − | 0.897845i | \(-0.645132\pi\) | ||||
−0.440312 | + | 0.897845i | \(0.645132\pi\) | |||||||
\(912\) | −4.00000 | −0.132453 | ||||||||
\(913\) | −29.0733 | −0.962186 | ||||||||
\(914\) | 12.3485 | 0.408452 | ||||||||
\(915\) | 62.4536 | 2.06465 | ||||||||
\(916\) | −22.6598 | −0.748702 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −23.6947 | −0.782043 | ||||||||
\(919\) | 16.2472 | 0.535947 | 0.267974 | − | 0.963426i | \(-0.413646\pi\) | ||||
0.267974 | + | 0.963426i | \(0.413646\pi\) | |||||||
\(920\) | 1.36814 | 0.0451062 | ||||||||
\(921\) | 3.85573 | 0.127051 | ||||||||
\(922\) | 32.6024 | 1.07370 | ||||||||
\(923\) | −2.11943 | −0.0697620 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.14221 | −0.300594 | ||||||||
\(926\) | 9.73023 | 0.319755 | ||||||||
\(927\) | 59.0367 | 1.93902 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | 21.6763 | 0.711177 | 0.355588 | − | 0.934643i | \(-0.384280\pi\) | ||||
0.355588 | + | 0.934643i | \(0.384280\pi\) | |||||||
\(930\) | −50.9821 | −1.67177 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 18.9002 | 0.619096 | ||||||||
\(933\) | −40.9478 | −1.34057 | ||||||||
\(934\) | 33.0234 | 1.08056 | ||||||||
\(935\) | −61.8020 | −2.02114 | ||||||||
\(936\) | −0.721733 | −0.0235906 | ||||||||
\(937\) | −40.3688 | −1.31879 | −0.659395 | − | 0.751797i | \(-0.729187\pi\) | ||||
−0.659395 | + | 0.751797i | \(0.729187\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.91630 | 0.127804 | ||||||||
\(940\) | −11.2804 | −0.367927 | ||||||||
\(941\) | 20.8571 | 0.679921 | 0.339960 | − | 0.940440i | \(-0.389586\pi\) | ||||
0.339960 | + | 0.940440i | \(0.389586\pi\) | |||||||
\(942\) | 61.4529 | 2.00224 | ||||||||
\(943\) | −2.57758 | −0.0839377 | ||||||||
\(944\) | −6.05523 | −0.197081 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.3220 | −0.563186 | ||||||||
\(947\) | −15.2163 | −0.494465 | −0.247232 | − | 0.968956i | \(-0.579521\pi\) | ||||
−0.247232 | + | 0.968956i | \(0.579521\pi\) | |||||||
\(948\) | −47.0075 | −1.52673 | ||||||||
\(949\) | −0.0684698 | −0.00222262 | ||||||||
\(950\) | −1.63791 | −0.0531407 | ||||||||
\(951\) | 35.1079 | 1.13845 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.12235 | −0.0687497 | −0.0343748 | − | 0.999409i | \(-0.510944\pi\) | ||||
−0.0343748 | + | 0.999409i | \(0.510944\pi\) | |||||||
\(954\) | −33.2124 | −1.07529 | ||||||||
\(955\) | −21.6249 | −0.699767 | ||||||||
\(956\) | −24.4945 | −0.792208 | ||||||||
\(957\) | 13.1633 | 0.425509 | ||||||||
\(958\) | −5.96752 | −0.192802 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6.84276 | 0.220849 | ||||||||
\(961\) | 24.5101 | 0.790649 | ||||||||
\(962\) | 1.25767 | 0.0405489 | ||||||||
\(963\) | 6.34332 | 0.204411 | ||||||||
\(964\) | 29.2268 | 0.941331 | ||||||||
\(965\) | −1.83816 | −0.0591725 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.4039 | −1.78167 | −0.890834 | − | 0.454328i | \(-0.849879\pi\) | ||||
−0.890834 | + | 0.454328i | \(0.849879\pi\) | |||||||
\(968\) | 11.6901 | 0.375735 | ||||||||
\(969\) | 20.9585 | 0.673282 | ||||||||
\(970\) | 11.5519 | 0.370909 | ||||||||
\(971\) | −21.2888 | −0.683190 | −0.341595 | − | 0.939847i | \(-0.610967\pi\) | ||||
−0.341595 | + | 0.939847i | \(0.610967\pi\) | |||||||
\(972\) | −17.4703 | −0.560359 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 22.4126 | 0.718146 | ||||||||
\(975\) | −0.486756 | −0.0155887 | ||||||||
\(976\) | 9.12695 | 0.292147 | ||||||||
\(977\) | −18.7651 | −0.600348 | −0.300174 | − | 0.953884i | \(-0.597045\pi\) | ||||
−0.300174 | + | 0.953884i | \(0.597045\pi\) | |||||||
\(978\) | −50.9821 | −1.63023 | ||||||||
\(979\) | −48.5488 | −1.55163 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39.5557 | 1.26292 | ||||||||
\(982\) | 12.5949 | 0.401920 | ||||||||
\(983\) | 33.1176 | 1.05629 | 0.528144 | − | 0.849155i | \(-0.322888\pi\) | ||||
0.528144 | + | 0.849155i | \(0.322888\pi\) | |||||||
\(984\) | −12.8918 | −0.410976 | ||||||||
\(985\) | −25.4285 | −0.810218 | ||||||||
\(986\) | −5.23961 | −0.166863 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.225322 | 0.00716845 | ||||||||
\(989\) | −2.00920 | −0.0638890 | ||||||||
\(990\) | 54.6878 | 1.73809 | ||||||||
\(991\) | −14.3450 | −0.455684 | −0.227842 | − | 0.973698i | \(-0.573167\pi\) | ||||
−0.227842 | + | 0.973698i | \(0.573167\pi\) | |||||||
\(992\) | −7.45051 | −0.236554 | ||||||||
\(993\) | −56.4738 | −1.79214 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.42242 | −0.0450936 | ||||||||
\(996\) | −16.8664 | −0.534432 | ||||||||
\(997\) | −20.3260 | −0.643730 | −0.321865 | − | 0.946786i | \(-0.604310\pi\) | ||||
−0.321865 | + | 0.946786i | \(0.604310\pi\) | |||||||
\(998\) | −39.7490 | −1.25823 | ||||||||
\(999\) | −36.5367 | −1.15597 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2842.2.a.r.1.4 | 4 | ||
7.6 | odd | 2 | 406.2.a.g.1.1 | ✓ | 4 | ||
21.20 | even | 2 | 3654.2.a.bg.1.3 | 4 | |||
28.27 | even | 2 | 3248.2.a.x.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
406.2.a.g.1.1 | ✓ | 4 | 7.6 | odd | 2 | ||
2842.2.a.r.1.4 | 4 | 1.1 | even | 1 | trivial | ||
3248.2.a.x.1.4 | 4 | 28.27 | even | 2 | |||
3654.2.a.bg.1.3 | 4 | 21.20 | even | 2 |